1. Surface area & volume UNIT 4

2. Prisms SECTION 1

3.  Prism: three dimensional shape with two parallel sides  Bases: sides parallel to each other  Lateral faces: sides that are not the bases PRISMS

4.  Volume = length × width × height  Example 1: Find the volume of a prism with a length of 5 inches, a width of 7 inches, and a height of 2 inches.  Example 2: Find the rectangular width of a prism with a volume of 72, a length of 6, and a height of 3. RECTANGULAR PRISM

5.  Example 3: Find the height (in terms of x) of a rectangular prism with a volume of 4x 2 – 8x – 32, a length of 4, and a width of x – 4.  Example 4: What is the longest line you can draw in this rectangular prism? CHALLENGE YOURSELF!

6. Pyramids SECTION 2

7. Lateral Side Base Height (Altitude) Lateral Height (“Slant height”)  One base is a regular polygon (all edges congruent)  Lateral faces are isosceles triangles  Lateral area = area of triangles added together PYRAMID

8.  Pyramid Volume = Bh  B = AREA of base  h = height  Pyramid lateral area = P l  P = Perimeter of base  l = Slant height  Ex.: Find the volume and lateral area of a pyramid with a square base with sides of 12 inches and a height of 8 inches. PYRAMID FORMULAS 1313 1212 Base 8 l = ? 12

9. Cylinders SECTION 3

10. CYLINDERS Base Lateral Area

11.  Volume = Bh  B = Area of base (B = πr 2 )  h = height  r = radius  Lateral Area = 2πrh  Examples:  Find the volume of a cylinder with a radius of 3 and a height of 10. Express your answer in terms of π.  Find the lateral area of the same cylinder. Round your answer to the nearest tenth. FORMULAS FOR A CYLINDER

12. Cones SECTION 4

13. CONES Base Lateral Area Lateral Height (“Slant” Height) Apex

14.  Volume = Bh  B = Area of base (B = πr 2 )  h = height, r = radius  Lateral Area = πr l  Where does this formula come from?  Find the lateral area and surface area of a cone with a diameter of 12 and a height of 8. Express your answer in terms of π.  Find the volume of the same cone to the nearest tenth. CONE FORMULAS 1313 8

15. Spheres SECTION 4

16. SPHERES Diameter

17.  Volume = πr 3  Surface Area = 4πr 2  Example: Find the volume of a sphere with a surface area of 144π. (Hint: Find the radius first!) SPHERE FORMULAS 4343